Note that while we construct the samples using earnings-deflated deviation thresholds
(i.e., 10 percent, 5 percent, and 2 percent) to alleviate the large error concern, we continue
to allocate the deviation based on segment sales (instead of segment profits) for two reasons.
First, to properly and fully allocate the total deviation, we require not only a positive
denominator but also a positive numerator for each segment. If we further exclude any
firms that have one or more segments with negative profits (i.e., negative numerators), we
would lose a prohibitively large portion of the sample. Second, the agency cost hypothesis
tests whether the poorly performing segments are more likely to be hidden; excluding all
the firms with negative earnings segments would yield a very low power test.